A ring is called nil G-*-clean ring if each of its elements is a sum of a G-projection and a nilpotent.In this paper,we study the basic properties of this ring and some relations with other rings.We prove that R is ni...A ring is called nil G-*-clean ring if each of its elements is a sum of a G-projection and a nilpotent.In this paper,we study the basic properties of this ring and some relations with other rings.We prove that R is nil G-*-clean if(G(R)+J)/J=G(R/J)=and only if is nil,and is nil G-*-clean.展开更多
A ring is said to be UR if every element can be written as the sum of a unit and a regular element. These rings are shown to be a unifying generalization of regular rings, clean rings and （S, 2）-ring~. Some relation...A ring is said to be UR if every element can be written as the sum of a unit and a regular element. These rings are shown to be a unifying generalization of regular rings, clean rings and （S, 2）-ring~. Some relations of these rings are studied and several properties of clean rings and （S, 2）-rings are extended. PAng extensions of UR-rings are also investigated.展开更多
基金Supported by Anhui Provincial Natural Science Foundation(2008085MA06)。
文摘A ring is called nil G-*-clean ring if each of its elements is a sum of a G-projection and a nilpotent.In this paper,we study the basic properties of this ring and some relations with other rings.We prove that R is nil G-*-clean if(G(R)+J)/J=G(R/J)=and only if is nil,and is nil G-*-clean.
基金the National -Natural Science Foundation of China （No. 10571026） the Natural Science Foundation of Jiangsu Province （No. 2005207）.
文摘A ring is said to be UR if every element can be written as the sum of a unit and a regular element. These rings are shown to be a unifying generalization of regular rings, clean rings and （S, 2）-ring~. Some relations of these rings are studied and several properties of clean rings and （S, 2）-rings are extended. PAng extensions of UR-rings are also investigated.
